Group #14668774 — subgroups

Subgroups — #14668774

Order 2816.

390 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622099	C₂	1	1	yes	maximal, characteristic
2	C₄×C₈×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	#13066693	C₂	1	4	yes	maximal
4	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₈×Dic₁₁	C₄	1	2	yes	—
8	C₂×C₈×Dic₁₁	C₂²	1	2	yes	—
9	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
10	C₄²×Dic₁₁	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₁⋊C₈	C₄	1	1	yes	characteristic
12	C₁₁×#346	C₄	1	4	yes	complemented
13	#10622099	C₄	1	4	yes	complemented
14	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₁₁	C₈	1	4	yes	—
18	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
19	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
20	C₂×C₁₁×C₁₆	—	2	4	no	—
21	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
22	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
24	C₈×Dic₁₁	—	2	4	no	—
25	C₈×Dic₁₁	—	2	4	no	—
26	C₂×C₁₁⋊C₁₆	—	2	4	no	—
27	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
28	C₄×C₁₁⋊C₈	C₈	1	4	yes	—
29	#12591	—	11	1	no	maximal, Sylow
30	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
31	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
32	C₂²×Dic₁₁	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₁	C₄²	1	2	yes	—
34	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
35	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₁	#41	1	4	yes	—
38	C₄²×C₁₁	C₄²	1	2	yes	—
39	C₄²×C₁₁	C₂×C₈	1	2	yes	—
40	C₄×Dic₁₁	—	2	8	no	—
41	C₄×Dic₁₁	—	2	2	no	—
42	C₄×Dic₁₁	—	2	2	no	—
43	C₂×C₁₁⋊C₈	—	2	2	no	—
44	C₂×C₁₁⋊C₈	—	2	2	no	—
45	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
46	C₁₁×C₁₆	—	2	4	no	—
47	C₁₁⋊C₁₆	—	2	4	no	—
48	C₂×#346	—	11	1	no	—
49	C₂×#346	D₁₁	1	1	yes	characteristic
50	C₄²×C₈	—	11	1	no	—
51	#1374	—	11	4	no	—
52	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₁	—	2	4	no	—
54	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
55	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
56	C₂×C₄×C₁₁	#117	1	2	yes	—
57	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
59	C₂×Dic₁₁	—	2	4	no	—
60	C₂×Dic₁₁	—	2	4	no	—
61	C₂×Dic₁₁	M₃₂	1	8	yes	—
62	C₈×C₁₁	#97	1	4	yes	—
63	C₈×C₁₁	#117	1	2	yes	—
64	C₈×C₁₁	#117	1	2	yes	—
65	C₁₁⋊C₈	—	2	4	no	—
66	C₂²×C₁₆	—	11	2	no	—
67	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
68	C₂×C₄×C₈	—	11	1	no	—
69	C₂×C₄×C₈	—	11	2	no	—
70	C₂×C₄×C₈	—	11	2	no	—
71	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
72	C₄³	—	11	1	no	—
73	#346	—	11	4	no	—
74	#346	Dic₁₁	1	4	yes	complemented
75	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
76	C₂²×C₁₁	#431	1	2	yes	—
77	C₂²×C₁₁	C₂×M₃₂	1	4	yes	—
78	C₄×C₁₁	—	2	4	no	—
79	C₄×C₁₁	#376	1	1	yes	characteristic
80	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
81	C₄×C₁₁	#431	1	2	yes	—
82	Dic₁₁	—	2	8	no	—
83	C₂²×C₈	—	11	2	no	—
84	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
85	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
86	C₂×C₄²	—	11	4	no	—
87	C₂×C₄²	—	11	2	no	—
88	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
89	C₂×C₁₆	—	2	4	no	—
90	C₂×C₁₆	—	11	4	no	—
91	C₂×C₁₆	—	22	4	no	—
92	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
93	C₄×C₈	—	11	4	no	—
94	C₄×C₈	—	22	4	no	—
95	C₄×C₈	—	22	4	no	—
96	C₄×C₈	C₄×D₁₁	1	2	yes	—
97	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
98	C₂×C₁₁	#1744	1	1	yes	characteristic
99	C₂×C₁₁	C₄×M₃₂	1	2	yes	—
100	C₂×C₁₁	#2163	1	4	yes	—
101	C₂²×C₄	—	11	4	no	—
102	C₂²×C₄	C₈×D₁₁	1	2	yes	—
103	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
104	C₂×C₈	—	11	4	no	—
105	C₂×C₈	—	22	2	no	—
106	C₂×C₈	—	22	2	no	—
107	C₂×C₈	#4313	1	4	yes	—
108	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
109	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
110	C₂×C₈	#4339	1	4	yes	—
111	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
112	C₄²	—	22	8	no	—
113	C₄²	—	22	2	no	—
114	C₄²	—	22	2	no	—
115	C₄²	C₈×D₁₁	1	2	yes	—
116	C₄²	C₄×Dic₁₁	1	2	yes	—
117	C₁₆	—	2	4	no	—
118	C₁₆	—	22	4	no	—
119	C₁₁	#12591	1	1	yes	characteristic, complemented, Sylow
120	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
121	C₂×C₄	—	2	4	no	—
122	C₂×C₄	—	11	8	no	—
123	C₂×C₄	—	22	4	no	—
124	C₂×C₄	—	22	4	no	—
125	C₂×C₄	C₈×Dic₁₁	1	4	yes	—
126	C₂×C₄	#66925	1	2	yes	—
127	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
128	C₂×C₄	C₂×#4313	1	2	yes	—
129	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
130	C₈	—	22	4	no	—
131	C₈	#66879	1	4	yes	—
132	C₈	#66925	1	2	yes	—
133	C₈	#66979	1	2	yes	—
134	C₂²	#10622298	1	2	yes	—
135	C₂²	D₁₁×M₃₂	1	4	yes	—
136	C₂²	C₂×C₈×Dic₁₁	1	1	yes	characteristic
137	C₄	—	2	4	no	—
138	C₄	—	22	8	no	—
139	C₄	#10622298	1	2	yes	—
140	C₄	#10622545	1	1	yes	characteristic
141	C₄	C₂×#66879	1	1	yes	characteristic
142	C₂	#13068361	1	1	yes	characteristic
143	C₂	M₃₂×Dic₁₁	1	2	yes	—
144	C₂	#13070417	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10622099

C₂

yes

maximal, characteristic

C₄×C₈×Dic₁₁

C₂

yes

maximal, characteristic

#13066693

C₂

yes

maximal

C₂×C₁₁×#346

C₂

yes

maximal, characteristic

C₂²×C₁₁×C₁₆

C₂²

yes

—

C₂×C₄×C₈×C₁₁

C₂²

yes

characteristic

C₂×C₈×Dic₁₁

C₄

yes

—

C₂×C₈×Dic₁₁

C₂²

yes

—

C₂²×C₁₁⋊C₁₆

C₂²

yes

—

C₄²×Dic₁₁

C₄

yes

characteristic

C₂×C₄×C₁₁⋊C₈

C₄

yes

characteristic

C₁₁×#346

C₄

yes

complemented

#10622099

C₄

yes

complemented

C₂²×C₈×C₁₁

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₁

C₂³

yes

characteristic

C₂×C₄²×C₁₁

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₁

C₈

yes

—

C₂×C₄×Dic₁₁

C₂×C₄

yes

—

C₂²×C₁₁⋊C₈

C₂×C₄

yes

—

C₂×C₁₁×C₁₆

—

C₂×C₁₁×C₁₆

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₄×C₈×C₁₁

C₂×C₄

yes

—

C₈×Dic₁₁

—

C₈×Dic₁₁

—

C₂×C₁₁⋊C₁₆

—

C₂×C₁₁⋊C₁₆

C₂×C₄

yes

—

C₄×C₁₁⋊C₈

C₈

yes

—

#12591

—

maximal, Sylow

C₂²×C₄×C₁₁

C₂×C₈

yes

—

C₂²×C₄×C₁₁

C₂²×C₄

yes

characteristic

C₂²×Dic₁₁

C₂×C₈

yes

—

C₂×C₈×C₁₁

C₄²

yes

—

C₂×C₈×C₁₁

M₁₆

yes

—

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₁

#41

yes

—

C₄²×C₁₁

C₄²

yes

—

C₄²×C₁₁

C₂×C₈

yes

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₄×Dic₁₁

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

—

C₂×C₁₁⋊C₈

C₂×C₈

yes

—

C₁₁×C₁₆

—

C₁₁⋊C₁₆

—

C₂×#346

—

C₂×#346

D₁₁

yes

characteristic

C₄²×C₈

—

#1374

—

C₂³×C₁₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₁

—

C₂×C₄×C₁₁

C₄×C₈

yes

—

C₂×C₄×C₁₁

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₁

#117

yes

—

C₂×C₄×C₁₁

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₁

C₂×M₁₆

yes

—

C₂×Dic₁₁

—

C₂×Dic₁₁

—

C₂×Dic₁₁

M₃₂

yes

—

C₈×C₁₁

#97

yes

—

C₈×C₁₁

#117

yes

—

C₈×C₁₁

#117

yes

—

C₁₁⋊C₈

—

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₁₁

yes

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₁

yes

characteristic

C₄³

—

#346

—

#346

Dic₁₁

yes

complemented

C₂²×C₁₁

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₁

#431

yes

—

C₂²×C₁₁

C₂×M₃₂

yes

—

C₄×C₁₁

—

C₄×C₁₁

#376

yes

characteristic

C₄×C₁₁

C₂×#97

yes

characteristic

C₄×C₁₁

#431

yes

—

Dic₁₁

—

C₂²×C₈

—

C₂²×C₈

C₄×D₁₁

yes

characteristic

C₂²×C₈

C₂²×D₁₁

yes

characteristic

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₄×D₁₁

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×Dic₁₁

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₄×D₁₁

yes

—

C₄×C₈

C₂×Dic₁₁

yes

—

C₂×C₁₁

#1744

yes

characteristic

C₂×C₁₁

C₄×M₃₂

yes

—

100

C₂×C₁₁

#2163

yes

—

101

C₂²×C₄

—

102

C₂²×C₄

C₈×D₁₁

yes

—

103

C₂²×C₄

C₂×C₄×D₁₁

yes

characteristic

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

#4313

yes

—

108

C₂×C₈

C₄×Dic₁₁

yes

—

109

C₂×C₈

C₂×C₄×D₁₁

yes

characteristic

110

C₂×C₈

#4339

yes

—

111

C₂×C₈

C₂²×Dic₁₁

yes

characteristic

112

C₄²

—

113

C₄²

—

114

C₄²

—

115

C₄²

C₈×D₁₁

yes

—

116

C₄²

C₄×Dic₁₁

yes

—

117

C₁₆

—

118

C₁₆

—

119

C₁₁

#12591

yes

characteristic, complemented, Sylow

120

C₂³

C₂×C₈×D₁₁

yes

characteristic

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

C₈×Dic₁₁

yes

—

126

C₂×C₄

#66925

yes

—

127

C₂×C₄

C₂×C₈×D₁₁

yes

characteristic

128

C₂×C₄

C₂×#4313

yes

—

129

C₂×C₄

C₂×C₄×Dic₁₁

yes

characteristic

130

C₈

—

131

C₈

#66879

yes

—

132

C₈

#66925

yes

—

133

C₈

#66979

yes

—

134

C₂²

#10622298

yes

—

135

C₂²

D₁₁×M₃₂

yes

—

136

C₂²

C₂×C₈×Dic₁₁

yes

characteristic

137

C₄

—

138

C₄

—

139

C₄

#10622298

yes

—

140

C₄

#10622545

yes

characteristic

141

C₄

C₂×#66879

yes

characteristic

142

C₂

#13068361

yes

characteristic

143

C₂

M₃₂×Dic₁₁

yes

—

144

C₂

#13070417

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₁₁
commutator	C₂²×C₁₁	C₂×C₄×C₈
Fitting	C₂×C₁₁×#346	C₂
socle, prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#12591
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×#346

subgroup

G/H

center, Frattini

C₂²×C₈

C₂²×D₁₁

commutator

C₂²×C₁₁

C₂×C₄×C₈

Fitting

C₂×C₁₁×#346

C₂

socle, prime radical

C₂³×C₁₁

C₂²×C₈

cosocle

C₂²×C₈×C₁₁

C₂³

D₁₁

C₁₁

G ▷ C₂²×C₁₁ ▷ C₁₁

C₁ ◁ C₂²×C₈ ◁ C₂×#346

N	H ≅ G/N	type
12. C₁₁×#346	C₄	semidirect
13. #10622099	C₄	semidirect
74. #346	Dic₁₁	semidirect
119. C₁₁	#12591	semidirect

H ≅ G/N

type

12. C₁₁×#346

C₄

semidirect

13. #10622099

C₄

semidirect

74. #346

Dic₁₁

semidirect

119. C₁₁

#12591

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10622099	2
C₄×C₈×Dic₁₁	2
#13066693	2
C₂×C₁₁×#346	2
#12591	11

subgroup

index

C₂×#10622099

C₄×C₈×Dic₁₁

#13066693

C₂×C₁₁×#346

#12591

Subgroups — #14668774

Conjugacy classes of subgroups

Complements

Maximal subgroups